Re: experts in small probabilities

"Bob Dole" <tsdev@xxxxxxxxxxxx> wrote in news:1137593943.196210.83690
@g44g2000cwa.googlegroups.com:

> Another rule of thumb that may be interesting is the confidence
> interval for non-occurrence. A nice reference for this is Robert
> Winkler, J.E. Smith, D.G. Fryback in American Statistician, February
> 2002, pages 1-4:
>
> "The 'Rule of 3' states that 3/n is a good approximation for an upper
> 95% confidence bound for p when we have seen n independent trials with
> no occurrence of the event of interest. The rule of 3 approximation is
> quite simple and very accurate for large n."
>
I first saw that rule in Hanley, J. A., and Lippman-Hand, A. (1983), "If
Nothing Goes Wrong, Is Everything All Right? Interpreting Zero
Numerators," Journal of the American Medical Association, 249, 1743?1745.

The rule was modified by Richard Browne in a manner that removes the need
for n to be large:
"To avoid confusion, we want a simple enhancement of the 3/nformula, and
one that could be easily remembered and used away from a computer. The
Bayesian Rule of Three of 3/(n + b) (Jovanovic and Levy, 1997) seems a
reasonable alternative form for an enhanced rule. By simple search
methods, I found that 3=(n+ 1.7) underestimates p95 by less than 1% for
all n > 3 and overestimates p95 by 1.1% for n = 3. I would hope that this
Modified Rule of Three could be disseminated as a preferred alternative
to 3/n." American Statistician, August 2002, Vol. 56, No. 3 p252

1) Jovanovic, B. D., and Levy, P. S. (1997), "A Look at the Rule of
Three,? The American Statistician, 51, 137?139.

--
David Winsemius

.